We should remark that the universal extension operator exists not only on smooth domains but also on Lipschitz domains. This is done by Rychkov [1]} using Littlewood-Paley decompositions. Rychkov's extension operator \(E^R\)  has the form \(E^Rf=\sum _{j=0}^\infty \psi _j\ast (\mathbf {1}_{\mathbb {R}^n_+}\cdot (\phi _j\ast f))\)  where \(\mathbf {1}_{\mathbb {R}^n_+}\)  is the characteristic function of \(\mathbb {R}^n_+\)  and \((\phi _j,\psi _j)_{j=0}^\infty \)  is a carefully chosen family of Schwartz functions. The shape of \(E^R\)  is totally different from (REF ) and the construction follows a different methodology.
